German Philosophy of Mathematics from Gauss to Hilbert

Abstract

Suppose we were to ask some students of philosophy to imagine a typical book of classical German philosophy and describe its general style and character, how might they reply? I suspect that they would answer somewhat as follows. The book would be long and heavy, it would be written in a complicated style which employed only very abstract terms, and it would be extremely difficult to understand. At all events a description of this kind does indeed fit many famous works of German philosophy. Let us take for example Hegel'sPhenomenology of Spiritof 1807. The 1977 English translation published by Oxford has 591 pages, and as for style here is a typical passage:Self-consciousness found the Thing to be like itself, and itself to be like a Thing; i.e., it is aware that it isin itselfthe objectively real world. It is no longer theimmediatecertainty of being all reality, but a certainty for which the immediate in general has the form of something superseded, so that theobjectivityof the immediate still has only the value of something superficial, its inner being and essence being self-consciousness itself. The object, to which it is positively related, is therefore a self-consciousness. It is in the form of thinghood, i.e. it isindependent; but it is certain that this independent object is for it not something alien, and thus it knows that it isin principlerecognized by the object. It is Spirit which, in the duplication of its self-consciousness and in the independence of both, has the certainty of its unity with itself. This certainty has now to be raised to the level of truth; what holds good for itin principle, and in its inner certainty, has to enter into its consciousness and becomeexplicitfork. (p. 211)